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Chapter 3: BASEBAND PULSE AND DIGITAL SIGNALING

Chapter Objectives: • Analog-to-digital signaling (pulse code modulation )

Binary and multilevel digitals signals • Spectra and bandwidths of digital signals • Prevention of intersymbol interference • Time division multiplexing • Packet transmission

Huseyin BilgekulEeng360 Communication Systems I

Department of Electrical and Electronic Engineering Eastern Mediterranean University

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INTRODUCTIONINTRODUCTION

This chapter we study how to encode analog waveforms into base band digital signals. Digital signal is popular because of the low cost and flexibility.

Main goals: • To study how analog waveforms can be converted to digital

waveforms, Pulse Code Modulation.

• To learn how to compute the spectrum for digital signals.

• Examine how the filtering of pulse signals affects our ability to recover the digital information. Intersymbol interference (ISI).

• To study how we can multiplex (combine) data from several digital bit streams into one high-speed digital stream for transmission over a digital system Time-division Multiplexing.

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PULSE AMPLITUDE MODULATIONPULSE AMPLITUDE MODULATION

Pulse Amplitude Modulation (PAM) is used to describe the conversion of the analog signal to a pulse-type signal in which the amplitude of the pulse denotes the analog information.

The purpose of PAM signaling is to provide another waveform that looks like pulses, yet contains the information that was present in the analog waveform.

There are two classes of PAM signals: • PAM that uses Natural Sampling (gating); • PAM that uses Instantaneous Sampling to produce a flat-top

pulse.

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Natural Sampling (Gating)Natural Sampling (Gating)

DEFINTION: If w(t) is an analog waveform bandlimited to B hertz, the PAM signal that uses natural sampling (gating) is

ws(t) =w(t)s(t) Where

S(t) is a rectangular wave switching waveform and fs = 1/Ts ≥ 2B.

THEORM: The spectrum for a naturally sampled PAM signal is:

• Where fs= 1/Ts, ωs = 2π fs,• the Duty Cycle of s(t) is d = τ/Ts , • W(f)= F[w(t)] is the spectrum of the original unsampled waveform, • cn represents the Fourier series coefficients of the switching waveform.

sin( )( ) F[ ( )] ( ) ( )s s n s s

n n

ndW f w t c W f nf d W f nf

nd

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Natural Sampling (Gating)Natural Sampling (Gating)w(t)

ws(t) =w(t)s(t)

s(t)

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Generating Natural SamplingGenerating Natural Sampling

The PAM wave form with natural sampling can be generated using a

CMOS circuit consisting of a clock and analog switch as shown.

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Spectrum of Natural SamplingSpectrum of Natural Sampling

• The duty cycle of the switching waveform is d = τ/Ts = 1/3.

• The sampling rate is fs = 4B.

sin( )( ) F[ ( )] ( ) ( )s s n s s

n n

ndW f w t c W f nf d W f nf

nd

sin( )( ) ( )

sin( )

s sn

ndW f d W f nf

nd

ndd

nd

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Recovering Naturally Sampled Recovering Naturally Sampled PAM PAM At the receiver, the original analog waveform, w(t), can be recovered

from the PAM signal, ws(t), by passing the PAM signal through a low-pass filter where the cutoff frequency is: B <fcutoff < fs -B

If the analog signal is under sampled fs < 2B, the effect of spectral overlapping is called Aliasing. This results in a recovered analog signal that is distorted compared to the original waveform.

LPF FilterB <fcutoff < fs -B

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Demodulation of PAM SignalDemodulation of PAM Signal The analog waveform may be recovered from the PAM signal

by using product detection,

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Instantaneous Sampling (Flat-Top PAM)

• This type of PAM signal consists of instantaneous samples.

• w(t) is sampled at t = kTs .

• The sample values w(kTs ) determine the amplitude of the flat-top rectangular pulses.

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Instantaneous Sampling (Flat-Top PAM)

DEFINITION: If w(t) is an analog waveform bandlimited to B Hertz, the instantaneous sampled PAM signal is given by

– Where h(t) denotes the sampling-pulse shape and, for flat-top sampling, the pulse shape is,

THEOREM: The spectrum for a flat-top PAM signal is:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )s s s s s sk k k

w t w kT h t kT h t w kT t kT h t w t t kT

1( ) ( ) ( )

sin( ) ( )

s sks

W f H f W f nfT

fH f h t

f

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The spectrum of the flat-top The spectrum of the flat-top PAMPAM Analog signal maybe recovered from the flat-top PAM signal by the use of a LPF.

LPF Response

Note that the recovered signal has some distortions due to the curvature of the H(f).

Distortions can be removed by using a LPF having a response 1/H(f).

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Some notes on PAMSome notes on PAM• The flat-top PAM signal could be generated by using a sample-

and-hold type electronic circuit.• There is some high frequency loss in the recovered analog

waveform due to filtering effect H(f) caused by the flat top pulse shape.

• This can be compensated (Equalized) at the receiver by making the transfer function of the LPF to 1/H(f)

• This is a very common practice called “EQUALIZATION”• The pulse width τ is called the APERTURE since τ/Ts determines

the gain of the recovered analog signal

Disadvantages of PAM• PAM requires a very larger bandwidth than that of the original signal; • The noise performance of the PAM system is not satisfying.